Elliptic curve isogeny class with Cremona label 193600fa (LMFDB label 193600.ix)

• Label: 193600fa
• Number of curves: $4$
• Conductor: $193600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 193600fa have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 193600fa do not have complex multiplication.

Modular form 193600.2.a.fa

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 193600fa

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
193600.ix4	193600fa1	\([0, -1, 0, -548533, 153346437]\)	\(643956736/15125\)	\(428717762000000000\)	\([2]\)	\(3317760\)	\(2.1688\)	\(\Gamma_0(N)\)-optimal
193600.ix3	193600fa2	\([0, -1, 0, -1214033, -290542063]\)	\(436334416/171875\)	\(77948684000000000000\)	\([2]\)	\(6635520\)	\(2.5154\)
193600.ix2	193600fa3	\([0, -1, 0, -5388533, -4751993563]\)	\(610462990336/8857805\)	\(251074270137680000000\)	\([2]\)	\(9953280\)	\(2.7181\)
193600.ix1	193600fa4	\([0, -1, 0, -85914033, -306481042063]\)	\(154639330142416/33275\)	\(15090865222400000000\)	\([2]\)	\(19906560\)	\(3.0647\)